Active front-end rectifier filter delay compensation method based on model predictive control

ABSTRACT

An active front-end rectifier filter delay compensation method based on model predictive control is disclosed. The method includes following steps: detecting a three-phase grid voltage and three-phase input current sampling value of an active front-end rectifier, and transforming both via Clarke transformation to acquire grid voltage sampling values e α  and e β , and input current sampling values i fα  and i fβ  under a two-phase stationary coordinate system; establishing an equivalent mathematical model of rectifier on the basis of voltage balancing equation (1) in an actual rectifier, and establishing an equivalent filter model on the basis of a transfer function corresponding to the actual filter, thus constituting a filter delay observer; and, compensating the difference value between the input current sampling values i fα  and i fβ , and equivalent current sampling values i ofα  and i ofβ  into an input of the filter delay observer via a proportional controller. In comparison to the input current sampling values i fα  and i fβ , the input current observed values i oα  and i oβ  of the rectifier are not impacted by a filter latency and are closer to the actual input current value of the rectifier such that the impact of the filter delay is compensated.

FIELD OF THE INVENTION

The present invention relates to a filter delay compensation method for an active front-end rectifier based on model predictive control, and belongs to the technical field of power electronic control.

BACKGROUND OF THE INVENTION

The power convertor all-digital control method based on model predictive control has grown rapidly in recent years. MPC (Model predictive control) is a mathematical-model-based control algorithm used for predicting the future response of object to be controlled. The algorithm comprises a value function defined according to the object to be controlled. By minimizing the value function, the optimal voltage vector is obtained for the algorithm during each sampling-period according to sampling-period prediction, and the optimal voltage vector is regarded as the interaction vector for the next period. MPC belongs to a non-linear control technique, and has fast transient response speed due to its no inclusion of linear controller and modulation algorithms. With the fast development of the micro processor and in-depth researching of the relevant techniques, MPC shows great advantages in the application of power electronics and motor driving fields.

MPC is a control algorithm for directly predicting and modulating current, and demands for a higher accuracy for the current to be detected. For eliminating interference, filtering process should be performed to the detected voltage and current signal prior sampling, but the filter will create signal delay while filtering high-frequency interference signal. As the MPC adopts circulation for optimization and non-constant-frequency control mode of outputting directly without modulation, the MPC has the advantage of fast transient response speed, but also has the disadvantages of high sampling frequency, and the system delay, thus affecting the operating performance. When the cut-off frequency of filter is low, signal filtering will suffer from some delay and produce variation between actual output value and set value of system, and further will impact the control effect. Therefore, it is necessary for us to develop a filter delay compensation method for MPC.

SUMMARY OF THE INVENTION

To solve the technical problems in the prior art MPC, the present invention provides a filter delay compensation method for an active front-end rectifier based on model predictive control. The method can effectively eliminate the filter delay impacts on the control system without adding additional equipment, and can remain a better control effects for the active front-end rectifier based on MPC even when a long delay exists in the system.

For solving the above technical problems, the present invention provides a technical scheme as follows:

A filter delay compensation method for an active front-end rectifier based on model predictive control, includes the following steps:

Step 1: detecting a three-phase grid voltage and three-phase input current sampling values of an active front-end rectifier, and transforming both via Clarke transformation to acquire grid voltage sampling values e_(α) and e_(β), and input current sampling values i_(fα) and i_(fβ) under a two-phase stationary coordinate system;

Step 2: establishing an equivalent mathematical model of rectifier on the basis of the voltage balancing equation (1) in an actual rectifier;

$\begin{matrix} \left\{ \begin{matrix} {e_{\alpha} = {u_{\alpha} + {Ri}_{\alpha} + {L\frac{\mathbb{d}i_{\alpha}}{\mathbb{d}t}}}} \\ {e_{\beta} = {u_{\beta} + {Ri}_{\beta} + {L\frac{\mathbb{d}i_{\beta}}{\mathbb{d}t}}}} \end{matrix} \right. & (1) \end{matrix}$

Wherein, e_(α) and e_(β) are grid voltage sampling values, i_(α) and i_(β) are input current values of the rectifier; L and R are input inductance values and equivalent series resistance value respectively; u_(α) and u_(β) are input voltage values of rectifier;

Establishes an equivalent filter model on the basis of the transfer function corresponding to the actual filter, wherein the ideal transfer function thereof is equation (2) of:

$\begin{matrix} {{F(s)} = \frac{{b_{m}s^{m}} + {b_{m - 1}s^{m - 1}} + \ldots + b_{0}}{{a_{n}s^{n}} + {a_{n - 1}s^{n - 1}} + \ldots + a_{0}}} & (2) \end{matrix}$

wherein, a₀, a₁ . . . a_(n) are coefficient of part-denominator of transfer function to the filter; b₀, b₁ . . . b_(m) are coefficient of part-numerator of transfer function to the filter; s is the complex variable of transfer function;

The above equivalent mathematical model of rectifier and equivalent filter model constitute a filter delay observer;

Step 3: taking the grid voltage sampling values e_(α) and e_(β) acquired by step 1 and the rectifier input voltage values u_(α) and u_(β) acquired by the last sampling period as the input value of the filter delay observer; and obtaining the equivalent rectifier input current values i_(oα) and i_(oβ) by equivalent mathematical model of rectifier;

Step 4: putting equivalent rectifier input current values i_(oα) and i_(oβ) into the equivalent filter model, and obtaining equivalent sampling current values i_(ofα) and i_(ofβ);

Step 5: compensating the difference value between the input current sampling values i_(fα) and i_(fβ) acquired by step 1 and equivalent current sampling values i_(ofα) and i_(ofβ) acquired by step 4 into an input of the filter delay observer via a proportional controller;

Step 6: inputting the equivalent rectifier input current values i_(oα) and i_(oβ) which are regarded as the rectifier input current observed values into the model predictive control algorithm, and achieving the optimal switching state and the corresponding rectifier input voltage values u_(α) and u_(β); in comparison to the input current sampling values i_(fα) and i_(fβ), the input current observed values i_(oα) and i_(oβ) of the rectifier are not impacted by the filter delay and are closer to the actual input current value of the rectifier, as such, the impact of the filter delay is compensated.

Compared with the prior art, the advantages of the present invention are:

Without changing the hardware structure, the present invention can effectively eliminate the filter delay impacts on the MPC algorithm via adding filter delay observer. When there exists a long delay in the active front-end rectifier control system, the method still can effectively eliminate the current harmonic, thus improving the control quality and robustness of the system, enhancing the MPC effects in the actual application, and realizing stable operation of the active front-end rectifier based on MPC when there exists a long delay.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a relational between a first-order filter cut-off frequency and signal delay;

FIG. 2 is a relational diagram of phase delay in different filter order under the cut-off frequency of 1 kHz;

FIG. 3 is a control flow diagram of MPC algorithm based on the filter delay observer; and

FIG. 4 is a control flow diagram of the filter delay observer.

DETAILED DESCRIPTION OF THE INVENTION

The present invention will be described in detail in combination with the accompanying embodiments.

A filter delay compensation method for an active front-end rectifier based on model predictive control, includes the following steps:

Step 1: detecting a three-phase grid voltage and three-phase input current sampling values of an active front-end rectifier, and transforming both via Clarke transformation to acquire grid voltage sampling values e_(α) and e_(β), and input current sampling values i_(fα) and i_(fβ) under a two-phase stationary coordinate system;

Step 2: establishing an equivalent mathematical model of rectifier on the basis of the voltage balancing equation (1) in an actual rectifier;

$\begin{matrix} \left\{ \begin{matrix} {e_{\alpha} = {u_{\alpha} + {Ri}_{\alpha} + {L\frac{\mathbb{d}i_{\alpha}}{\mathbb{d}t}}}} \\ {e_{\beta} = {u_{\beta} + {Ri}_{\beta} + {L\frac{\mathbb{d}i_{\beta}}{\mathbb{d}t}}}} \end{matrix} \right. & (1) \end{matrix}$

wherein, e_(α) and e_(β) are grid voltage sampling values, i_(α) and i_(β) are input current values of the rectifier; L and R are input inductance values and equivalent series resistance value respectively; u_(α) and u_(β) are input voltage values of rectifier;

Establishes an equivalent filter model on the basis of the transfer function corresponding to the actual filter, and the ideal transfer function thereof is equation (2) of:

$\begin{matrix} {{F(s)} = \frac{{b_{m}s^{m}} + {b_{m - 1}s^{m - 1}} + \ldots + b_{0}}{{a_{n}s^{n}} + {a_{n - 1}s^{n - 1}} + \ldots + a_{0}}} & (2) \end{matrix}$

wherein, a₀, a₁ . . . a_(n) are coefficient of part-denominator of transfer function to the filter; b₀, b₁ . . . b_(m) are coefficient of part-numerator of transfer function to the filter; and s is the complex variable of transfer function;

The above equivalent mathematical model of rectifier and equivalent filter model constitute a filter delay observer;

Step 3: taking the grid voltage sampling values e_(α) and e_(β) acquired by step 1 and the rectifier input voltage values u_(α) and u_(β) acquired by the last sampling period as the input value of the filter delay observer; and obtaining the equivalent rectifier input current values i_(oα) and i_(oβ) by equivalent mathematical model of rectifier;

Step 4: putting equivalent rectifier input current values i_(oα) and i_(oβ) into the equivalent filter model, and obtaining equivalent sampling current values i_(ofα) and i_(ofβ);

Step 5: compensating the difference value between the input current sampling values i_(fα) and i_(fβ) acquired by step 1 and equivalent current sampling values i_(ofα) and i_(ofβ) acquired by step 4 into an input of the filter delay observer via a proportional controller;

Step 6: inputting the equivalent rectifier input current values i_(oα) and i_(oβ) which are regarded as the rectifier input current observed values into the model predictive control algorithm, and achieving the optimal switching state and the corresponding rectifier input voltage values u_(α) and u_(β); in comparison to the input current sampling values i_(fα) and i_(fβ), the input current observed values i_(oα) and i_(oβ) of the rectifier are not impacted by the filter delay and are closer to the actual input current value of the rectifier, as such, the impact of the filter delay is compensated.

The present invention will be described in detail in combination with the accompanying drawings and embodiments.

The input filter will result in signal delay while filtering high frequency interference signal. FIG. 1 illustrates a relationship between a first-order filter cut-off frequency and signal delay. As shown in FIG. 1, filter delay increases with the decrease of cut-off frequency. FIG. 2 is a relational diagram of phase delay in different filter order when the cut-off frequency is 1 kHz. It can be seen from FIG. 2 that in comparison to the low order filters, high order filter produces longer delay.

FIG. 3 is a control flow diagram of MPC algorithm based on the filter delay observer, and the control method includes the following steps:

(1) After sensor measurement, low-pass filter filtering and analog quantity/digital quantity transformation, obtaining the active front-end rectifier three-phase grid voltage sampling values e_(a) and e_(b) and e_(c), three-phase current sampling values i_(fa), i_(fb) and i_(fc), and DC bus voltage sampling value u_(dc);

(2) Transforming the three-phase grid voltage sampling values e_(a) and e_(b) and e_(c), and three-phase input current sampling values i_(fa), i_(ib) and i_(fc) obtained in step (1) via Clarke transformation (3φ/αβ transforming module in FIG. 3) to acquire grid voltage sampling values e_(α) and e_(β), and input current sampling values i_(fα) and i_(fβ) under a two-phase stationary coordinate system;

(3) Arranging the three-phase grid voltage sampling values e_(a) and e_(b) and e_(c) such that they pass through phase-locked loop, and achieving grid voltage angle θ;

(4) Performing the operating of subtraction between the DC bus voltage reference value u_(dc)* and DC bus voltage sampling value u_(dc) acquired by step (1), and the controller obtains the current reference value i_(d)* of d-axis in synchronously rotating reference frame via proportional integral. Assuming the current reference value of q-axis is 0, and grid voltage angle as the transforming angle, performing reverse PARK transforming (dq/αβ transforming module in FIG. 3) to current reference value i_(d)* and i_(d)* of d-axis and q-axis, and to acquire current reference values i_(α)* and i_(β)* under a two-phase stationary coordinate system;

(5) taking the rectifier input voltage values u_(αβ) computed by the step (6) of the last sampling period, grid voltage sampling values e_(α) and e_(β) acquired by step (2) and the input current sampling values i_(fα) and i_(fβ) as the input value of the filter delay observer; and obtaining the rectifier input current observed values i_(oα) and i_(oβ);

(6) taking the current reference values i_(α)* and i_(β)* acquired by step (4), grid voltage sampling values e_(α) and e_(β) acquired by step (2) and the rectifier input current observed values i_(oα) and i_(oβ) acquired by the step (5) as the input values of the MPC algorithm. Regarding to 8 kinds of switching states sequenced from 0 to 7, the rectifier input voltage values u_(α) and u_(β) and the corresponding optimal switching state signal S_(k) are obtained according to equations 3 and 4;

$\begin{matrix} \left\{ \begin{matrix} {{i_{\alpha,n}^{p}\left( {k + 1} \right)} = {{\frac{T}{L}\left\lbrack {{e_{\alpha}(k)} - {u_{\alpha,n}(k)} - {{Ri}_{o\;\alpha}(k)}} \right\rbrack} + {i_{o\;\alpha}(k)}}} \\ {{i_{\beta,n}^{p}\left( {k + 1} \right)} = {{\frac{T}{L}\left\lbrack {{e_{\beta}(k)} - {u_{\beta,n}(k)} - {{Ri}_{o\;\beta}(k)}} \right\rbrack} + {i_{o\;\beta}(k)}}} \end{matrix} \right. & (3) \end{matrix}$

Wherein, n=0, 1, . . . , 7; the values of i_(α,n) ^(p)(k+1)

i_(β,n) ^(p)(k+1) are the corresponding predicted current values of the 8 kinds of switching states sequenced from 0 to 7 in the next sampling period; T is the sampling period value; L is the input side filter inductance value; and R is the input side equivalent series resistance value. g _(n)(k+1)=[i _(α)*(k+1)−i _(α,n) ^(p)(k+1)]² +[i _(β)*(k+1)−i _(β,n) ^(p)(k+1)]²   (4)

Wherein, n=0, 1, . . . , 7; the values of g_(n) (k+1) are the results of the corresponding value function of the 8 kinds of switching states sequenced from 0 to 7. S _(k):min{g _(n)(k+1)}_(n=0,1, . . . ,?)  (5)

(7) Taking the optimal switching state signal S_(k) acquired by step (6) as the switching signal of the power device, circulating to step (1) when the next sampling period starts.

The filter delay observer in FIG. 3 is shown in FIG. 4. The operation process is as follows:

Assume the grid voltage sampling values e_(α) and e_(β) are not affected by the filter. In the actual physical system (shown in the dashed box in the upper side of FIG. 3), grid voltage values e_(α) and e_(β) and rectifier input voltage values u_(α) and u_(β) act on the actual rectifier to obtain corresponding rectifier input current values i_(α) and i_(β), the values thereof then achieve the filtered input current sampling values i_(fα) and i_(fβ) via low-pass filter. In the observer (shown in the dashed box in the bottom side of FIG. 3), make model of the actual physical system to obtain the physical system model comprising equivalent mathematical models of rectifier and filter. The grid voltage values e_(α) and e_(β) and rectifier input voltage values u_(α) and u_(β) obtain the equivalent rectifier input current values i_(oα) and i_(oβ) via equivalent mathematical model of rectifier in the observer, and then obtain equivalent current sampling values i_(ofα) and i_(ofβ) of the physical system model via equivalent mathematical model of filter in the observer (namely of equivalent filter module in FIG. 3). In order to use the physical system model as an approximation for the actual physical system, compensate the difference value between the detected actual system current sampling values i_(fα) and i_(fβ) and equivalent current sampling values i_(ofα) and i_(ofβ) acquired by the physical system model into an input of the observer via a proportional controller (shown as Kp module in FIG. 3), to achieve the equivalent rectifier input current values i_(oα) and i_(oβ) as an approximation for the actual rectifier input current values i_(α) and i_(β). Therefore, use the equivalent rectifier input current values i_(oα) and i_(oβ) in place of the filtered input current sampling values i_(fα) and i_(fβ) as the sampling current values, and input the values into the model predictive control algorithm, thus avoiding the impacts of the filter delay.

The equivalent mathematical model in the observer algorithm approximates actual physical system, and the obtained equivalent rectifier input current values i_(oα) and i_(oβ) are equivalent to the actual input current values of the rectifier, thus effectively eliminating the sampling delay caused by filter.

Though various embodiments accompanied with drawings of the invention have been illustrated above, a person of ordinary skill in the art will understand that, variations and improvements made upon the illustrative embodiments fall within the scope of the invention, and the scope of the invention is only limited by the accompanying claims and their equivalents. 

The invention claimed is:
 1. A filter delay compensation method for an active front-end rectifier based on model predictive control, comprising the following steps: step 1: detecting a three-phase grid voltage and three-phase input current sampling values of an active front-end rectifier, and transforming both via Clarke transformation to acquire grid voltage sampling values e_(α) and e_(β), and input current sampling values i_(fα) and i_(fβ) under a two-phase stationary coordinate system; step 2: establishing an equivalent mathematical model of rectifier on the basis of the voltage balancing equation (1) in an actual rectifier; $\begin{matrix} \left\{ \begin{matrix} {e_{\alpha} = {u_{\alpha} + {Ri}_{\alpha} + {L\frac{\mathbb{d}i_{\alpha}}{\mathbb{d}t}}}} \\ {e_{\beta} = {u_{\beta} + {Ri}_{\beta} + {L\frac{\mathbb{d}i_{\beta}}{\mathbb{d}t}}}} \end{matrix} \right. & (1) \end{matrix}$ wherein, e_(α) and e_(β) are grid voltage sampling values, i_(α) and i_(β) are input current values of the rectifier; L and R are input inductance values and equivalent series resistance value respectively; and u_(α) and u_(β) are input voltage values of rectifier; establishing an equivalent filter model on the basis of the transfer function corresponding to the actual filter, wherein the ideal transfer function thereof is equation (2) of: $\begin{matrix} {{F(s)} = \frac{{b_{m}s^{m}} + {b_{m - 1}s^{m - 1}} + \ldots + b_{0}}{{a_{n}s^{n}} + {a_{n - 1}s^{n - 1}} + \ldots + a_{0}}} & (2) \end{matrix}$ wherein, a₀, a₁ . . . a_(n) are coefficient of part-denominator of transfer function to the filter; b₀, b₁ . . . b_(m) are coefficient of part-numerator of transfer function to the filter; and s is the complex variable of transfer function; the above equivalent mathematical model of rectifier and equivalent filter model constitute a filter delay observer; step 3: taking the grid voltage sampling values e_(α) and e_(β) acquired by step 1 and the rectifier input voltage values u_(α) and u_(β) acquired by the last sampling period as the input value of the filter delay observer; and obtaining the equivalent rectifier input current values i_(oα) and i_(oβ) by equivalent mathematical model of rectifier; step 4: putting equivalent rectifier input current values i_(oα) and i_(oβ) into the equivalent filter model, and obtaining equivalent sampling current values i_(ofα) and i_(ofβ); step 5: compensating the difference value between the input current sampling values i_(fα) and i_(fβ) acquired by step 1 and equivalent current sampling values i_(ofα) and i_(ofβ) acquired by step 4 into an input of the filter delay observer via a proportional controller; step 6: inputting the equivalent rectifier input current values i_(oα) and i_(oβ) which are regarded as the rectifier input current observed values into the model predictive control algorithm, and achieving the optimal switching state and the corresponding rectifier input voltage values u_(α) and u_(β); in comparison to the input current sampling values i_(fα) and i_(fβ), the input current observed values i_(oα) and i_(oβ) of the rectifier are not impacted by the filter delay and are closer to the actual input current value of the rectifier such that the impact of the filter delay is compensated. 